Banach algebra structure in Fourier spaces and generalization of harmonic analysis on locally compact groups
Masayuki FUJITA
著者情報
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Masayuki FUJITA
Department of Mathematical Sciences Faculty of Engineering Science Osaka University
ジャーナル
フリー
1979 年 31 巻 1 号 p. 53-67
詳細
- Published: 1979 Received: 1977/03/28 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
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訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文抄録 訂正内容: Wrong : Let (M, G, α) be a continuous W*-dynamical system. Then, the predual (G⊗αM)* of the crossed product G⊗αM of M by G can be turned into a Banach algebra and some of the notions and theorems in harmonic analysis on locally compact groups are extended to the corresponding ones in the crossed products. Among others, one can get a criterion for T in G⊗αM to fall in M: T=πα(x) for some x≠0 in M if and only if the support of T reduces to the unit e in G.
Right : Let (M, G, α) be a continuous W*-dynamical system. Then, the predual (G⊗αM)* of the crossed product G⊗αM of M by G can be turned into a Banach algebra and some of the notions and theorems in harmonic analysis on locally compact groups are extended to the corresponding ones in the crossed products. Among others, one can get a criterion for T in G⊗αM to fall in M: T=πα(x) for some x≠0 in M if and only if the support of T reduces to the unit e in G.
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報 訂正内容: Wrong : 1) J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, 2e édition, Gauthier-Villars, Paris, 1969.
2) J. Dixmier, Les C*-algèbres et leurs représentations, 2e édition, Gauthier-Villars, Paris, 1969.
3) P. Eymard, L'algèbres de Fourier d'un groupe localement compact, Bull. Soc. Math. France, 92 (1964), 181-236.
4) M. B. Landstad, Duality theory for covariant systems, Preprint.
5) Y. Nakagami, Dual action on a von Neumann algebra and Takasaki's duality, Kyushu Univ., Preprint.
6) K. Saito, On a duality for locally compact groups, Tohoku Math. J., 20 (1968), 355-367.
7) S. Stràtilà, D. Voiculescu and L. Zsido, On crossed product, I, Rev. Roumaine Math. Pures Appl., 21 (1976), 1411-1449.
8) H. Takai, On a Fourier expansion in continuous crossed products, Publ. Res. Inst. Math. Sci., 11 (1976), 849-880.
9) M. Takesaki, Duality for crossed products and the structure of von Neumann algebras of type III, Acta Math., 131 (1973), 249-310.
10) T. Turumaru, On the direct product of operator algebras III, Tohoku Math. J., 6 (1954), 208-211.
Right : [1] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, 2e édition, Gauthier-Villars, Paris, 1969.
[2] J. Dixmier, Les C-algèbres et leurs représentations, 2e édition, Gauthier-Villars, Paris, 1969.
[3] P. Eymard, L'algèbres de Fourier d'un groupe localement compact, Bull. Soc. Math. France, 92 (1964), 181-236.
[4] M. B. Landstad, Duality theory for covariant systems, Preprint.
[5] Y. Nakagami, Dual action on a von Neumann algebra and Takasaki's duality, Kyushu Univ., Preprint.
[6] K. Saitô, On a duality for locally compact groups, Tohoku Math. J., 20 (1968), 355-367.
[7] S. Stràtilà, D. Voiculescu and L. Zsido, On crossed product, I, Rev. Roumaine Math. Pures Appl., 21 (1976), 1411-1449.
[8] H. Takai, On a Fourier expansion in continuous crossed products, Publ. Res. Inst. Math. Sci., 11 (1976), 849-880.
[9] M. Takesaki, Duality for crossed products and the structure of von Neumann algebras of type III, Acta Math., 131 (1973), 249-310.
[10] T. Turumaru, On the direct product of operator algebras III, Tôhoku Math. J., 6 (1954), 208-211.
訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル 訂正内容: -
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